Regression beta

library(ggplot2)

rlt_theme <- theme(axis.title.y = element_text(colour="grey20",size=15,face="bold"),
        axis.text.x = element_text(colour="grey20",size=15, face="bold"),
        axis.text.y = element_text(colour="grey20",size=15,face="bold"),  
        axis.title.x = element_text(colour="grey20",size=15,face="bold"))+
        theme_bw()

---

Beta regression

El método presentado aquí es bastante innovador (2010 en adelante) y no van a encontrar mucha información en la literatura o el web sobre el método. Puede encontrar información suplementaria en el Vignette del paquete betareg.

Referencias:

Cribari-Neto, F., and Zeileis, A. (2010). Beta Regression in R. Journal of Statistical Software, 34(2), 1–24. http://www.jstatsoft.org/v34/i02/.

Grün, B., Kosmidis, I., and Zeileis, A. (2012). Extended Beta Regression in R: Shaken, Stirred, Mixed, and Partitioned. Journal of Statistical Software, 48(11), 1–25. http://www.jstatsoft. org/v48/i11/.

La regresión beta es una acercamiento GLM. La regresión beta es para modelar variables dependientes distribuidas con la distribución beta. Datos que tienen distribución beta incluye proporciones y razones, donde los valores se encuentra entre 0 y 1. Además de producir una regresión que máxima la verosimilitud (tanto para la media como para la precisión de una respuesta distribuida en beta), se proporcionan estimaciones con corrección de sesgo.

Los valores de la variable de respuesta deben estar entre 0 y 1, Si por consecuencia tiene valores que son 0 o 1, es necesario cambiarlo a 1= .999 y 0= 0.001. Los números no pueden ser 0 ni 1, deben ser mayores que 0 y menores que 1.

La paquete “betareg” y sus datos. Tenga en cuenta que este es el enfoque del modelo GLM con la respuesta a través de una función de enlace y un predictor lineal. Igual como GLM normal, existen numerosas funciones de enlace, que pueden ser útil como “logit”, “probit”, “cloglog”, “cauchit”, “log”, “loglog”.

Casi toda la información que se estará presentando aquí proviene de Cribari-Neto y Zeileis (Beta Regression in R).

Consulte el pdf, https://cran.r-project.org/web/packages/betareg/betareg.pdf para obtener una descripción del paquete y más detalles.

Estaré usando datos diferentes a lo que se presenta en el paquete para demostrar el valor de los análisis.

Primer paso, que es una distribución beta?

Lo más importante de la distribución beta es que los valores NUNCA son menores de 0 ni mayores de 1. En adición los intervalos de confianza tampoco no pueden ser ni menor de 0 ni mayor de 1.

library(tidyverse)
library(ggplot2)
library(betareg)

Aquí una serie de distribuciones beta. La distribución beta se calcula con dos parametros, shape 1 o \(\alpha\) y shape 2 o \(\beta\). No vamos a entrar en estos parámetros, aunque pueden ir a la pagina de Wikipedia para tener más información. Lo que deberian fijarse es que aparte de cuando hay un shape que es igual como Shape 1 = 0.5, y shape 2 = 0.5, (tambien shape 2 y 2) todas las otras distribuciones no son simétrica. Siempre hay una cola que se extiende en los valores pequeños o grandes.

library(ggplot2)

ggplot(betadj, aes(b1, cases, colour=beta_shapes))+
  geom_line()+
  ylim(0, 5)+
  scale_colour_discrete(name = "Beta_Shapes", labels = c("Shape 2 y 2", "Shape .5 y .5", "Shape 2 y 5", "Shape 8 y 1.5"))

Propoción de fumadores por diferentes paises. Los datos provienen de World Bank en el siguiente enlace, Smokers. Se encuentra información sobre 187 pais y la proporción de población mayor de 15 años que fuman

library(readr)
Proportion_smokers_world <- read_csv("Data/Proportion_smokers_world.csv")

## 
## ── Column specification ────────────────────────────────────────────────────────
## cols(
##   Country_Name = col_character(),
##   Country_Code = col_character(),
##   Indicator_Name = col_character(),
##   Indicator_Code = col_character(),
##   Y2000 = col_double(),
##   Y2005 = col_double(),
##   Y2010 = col_double(),
##   Y2011 = col_double(),
##   Y2012 = col_double(),
##   Y2013 = col_double(),
##   Y2014 = col_double(),
##   Y2015 = col_double(),
##   Y2016 = col_double()
## )

Smokers=Proportion_smokers_world 

Primero vamos a convertir los datos en proporción ya que el programa tiene que utilizar datos mayor de 0 y menor de 1. Seleccionamos el año 2000 y creamos un histograma de la distribución.

Smokers$Y2000P=(Smokers$Y2000)/100 # convertir en proporción

Convertir el promedio y varianza en shape

Convertir el promedio y la varianza de los datos en los valores del shape \(\alpha\) y \(\beta\). Se usa la siguiente para calcular los shapes. El \(\alpha\) referiere al promedio y \(\beta\) a la varianza. Usamos la siguiente función.

estBetaParams <- function(mu, var) {
  alpha <- ((1 - mu) / var - 1 / mu) * mu ^ 2
  beta <- alpha * (1 / mu - 1)
  return(params = list(alpha = alpha, beta = beta))
}
#mean(Smokers$Y2000P)
#var(Smokers$Y2000P)
estBetaParams((mean(Smokers$Y2000P)), (var(Smokers$Y2000P)))

## $alpha
## [1] 3.592488
## 
## $beta
## [1] 9.181559

Smokers$Y2000P=(Smokers$Y2000)/100 # convertir en proporción
x <- seq(0, 1, len = 100)

mean(Smokers$Y2000P)

## [1] 0.2812334

var(Smokers$Y2000P)

## [1] 0.01467551

ggplot(Smokers, aes(Y2000P))+
  geom_histogram(aes(y=..density..), colour="white", fill="grey50")+
  stat_function(aes(x = Smokers$Y2000P, y = ..y..), fun = dbeta, colour="red", n = 100,
                      args = list(shape1 = 3.593, shape2 = 9.185))+
  stat_function(fun = dnorm, 
                args = list(mean = mean(Smokers$Y2000P, na.rm = TRUE), 
                sd = sd(Smokers$Y2000P, na.rm = TRUE)), 
                colour = "green", size = 1)+
  xlab("Proportción de fumadores por Pais")+
  annotate("text", x = .5, y = 4.2, label = "Verde: dist Normal", color="darkgreen")+
  annotate("text", x = .5, y = 3.7, label = "Verde: dist Beta", color="red")

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Calculando el intervalo de confianza del promedio de una distribución beta. Se necesita los siguientes paquetes simpleboot , boot.

library(simpleboot)

## Simple Bootstrap Routines (1.1-7)

library(boot) # paquete para calcular el intervalo de confianza de una distribución beta
n=187 # El tamaño de muestra de los datos
alpha = 3.593 # estimado de la función arriba 
beta = 9.185
x = rbeta(n, alpha, beta)


x.boot = one.boot(x, median, R=10^4) # Aquí se usa la mediana, pq el promedio *mean* sera sesgado a la derecha.  
boot.ci(x.boot, type="bca")

## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 10000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = x.boot, type = "bca")
## 
## Intervals : 
## Level       BCa          
## 95%   ( 0.2385,  0.2893 )  
## Calculations and Intervals on Original Scale

Sobreponemos el intervalo de confianza de la mediana sobre la distribución beta

ggplot(Smokers, aes(Y2000P))+
  geom_histogram(aes(y=..density..), bins=20, colour="white", fill="grey50")+
  stat_function(aes(x = Smokers$Y2000P, y = ..y..), fun = dbeta, colour="red", n = 100,
                      args = list(shape1 = 3.593, shape2 = 9.185))+
  geom_vline(xintercept =0.2320, colour="blue")+ # El intervalo de confianza del promedio
  geom_vline(xintercept =0.2768, colour="blue")+
  rlt_theme+
  xlab("Proporción de fumadores por Pais")

Ahora vamos es hacer el primer análisis de regresión donde nuestra respuesta es una proporción.

library(ggversa) # paquete para los datos
attach(dipodium)
dipodium

Tree Number	Tree species	DBH	Plant number	Ramet number	Distance	Orientation	Number_of_Flowers	Height_Inflo	Herbivory	RowPosition_NF	Number_Flowers_position	Number_of_fruits	Perc_FR_set	pardalinum_or_roseum	Fruit_position_effect	Frutos_si_o_no	P_or_R_Infl_Lenght	Num of fruits	Species_Name	Cardinal orientation	PropFR
1	E.o	75	1	1	2.47	40	11	35	n	1	24	0	0	r	1	0	r	0	r	1	0.0001
1	E.o	76	2	1	1.97	50	19	47	n	2	23	0	0	r	2	0	r	0	r	2	0.0001
2	E.o	76	3	1	1.95	350	18	63	n	3	25	1	0.04	r	3	0	r	1	r	8	0.0401
3	E.o	58	4	1	3.24	210	24	47	n	4	20	5	0.25	r	4	0	r	5	r	5	0.25
4	E.o		5	1	0.85	80	25	61	n	5	13	0	0	r	5	0	r	0	r	2	0.0001
5	E.o	59	6	1	2.62	160	17	35	n	6	25	2	0.08	p	6	0	r	2	p	4	0.0801
5	E.o	59	7	1	2.82	170	19	51	n	7	20	0	0	p	7	0	r	0	p	4	0.0001
6	E.o	8	8	1	3.12	245	14	43	n	8	27	0	0	r	8	0	r	0	r	6	0.0001
7	E.o	11.5	9	1	1.12	208	16	42	n	9	27	1	0.037	r	9	0	r	1	r	5	0.0371
8	E.o	8.5	10	1	0.75	360	23	60	n	10	21	7	0.333	p	10	0	r	1	p	8	0.333
8	E.o	8.5	11	1	0.09	50	14	51	n	11	11	4	0.364	p	11	0	r	1	p	2	0.364
8	E.o	8.5	12	1	1.12	90	4	42	H	12	20	0	0	r	12	0	r	0	r	2	0.0001
8	E.o	8.5	12	2	1.12	90	23	61	n	13	30	0	0	r	13	0	r	0	r	2	0.0001
9	E.o	12	13	1	1.32	135	21	50	n	14	28	5	0.179	r	14	0	r	5	r	3	0.179
10	E.o	73	14	1	5.06	210	21	53	n	15	13	2	0.154	r	15	0	r	2	r	5	0.154
10	E.o	73	14	2	5.06	210	16	35	n	16	24	0	0	r	16	0	r	0	r	5	0.0001
10	E.o	73	14	3	5.06	210			H	17	24	5	0.208	r	17	0	r	5	r	5	0.208
11	E.o	73	15	1	4.16	322	13	44	n	18	28	1	0.0357	p	18	0	r	1	p	8	0.0358
12	E.o	16	16	1	1.32	125	33	79	n	19	26	4	0.154	r	19	0	r	4	r	3	0.154
12	E.o	16	16	1	1.32	125	15	60	n	20	9	0	0	r	20	0	r	0	r	3	0.0001
13	E.o	41	17	1	0.52	120	17	43	n	21	18	6	0.333	r	21	0	r	6	r	3	0.333
14	E.o	14	18	1	2.56	30	14	43	n	22	19	2	0.105	p	22	0	r	2	r	1	0.105
14	E.o	14	19	1	1.05	330	23	52	n	23	19	2	0.105	r	23	0	r	2	p	8	0.105
15	E.o	11	20	1	4.9	165	30	69	n	24	30	3	0.1	r	24	0	r	3	r	4	0.1
15	E.o	11	20	1	4.22	170	28	62	n	25	29	2	0.069	p	1	0	r	2	p	4	0.0691
16	E.o	84	21	1	1.66	220	18	45	n	26	19	0	0	r	2	0	r	0	r	5	0.0001
17	E.o	79	22	1	6.5	130	17	50	n	27	22	0	0	r	3	0	r	0	r	3	0.0001
17	E.o	79	23	1	3	115	35	63	n	28	20	5	0.25	r	4	0	r	5	r	3	0.25
17	E.o	79	24	1	2.8	115	13	34	n	29	32	3	0.0938	r	5	0	r	3	r	3	0.0939
17	E.o	79	25	1	1.3	215	30	73	n	30	13	2	0.154	r	6	0	r	2	r	5	0.154
18	E.o	79.5	26	1	0.5	250	32	67	n	31	27	3	0.111	r	7	0	r	3	r	6	0.111
19	E.o	84	27	1	2.22	20	21	65	n	32	11	3	0.273	r	8	0	r	3	r	1	0.273
20	E.o	84	28	1	2.38	80	28	72	n	33	32	0	0	r	9	0	r	0	r	2	0.0001
20	E.o	84	29	1	3.03	80	14	46	n	34	23	3	0.13	r	10	0	r	3	r	2	0.131
21	E.radiata	7	30	1	1.3	254	14	51	n	35	13	3	0.231	r	11	0	r	3	r	6	0.231
21	E.radiata	7	31	1	3.13	0	16	41	n	36	16	2	0.125	r	12	0	r	2	r	1	0.125
22	E.o	40	32	1	6.15	340	24	48	n	37	22	1	0.0455	r	13	0	r	1	r	8	0.0456
22	E.o	40	33	1	0.34	140	15	45	n	38	28	5	0.179	r	14	0	r	5	r	4	0.179
22	E.o	40	34	1	4.6	110	26	49	n	39	20	1	0.05	r	15	0	r	1	r	3	0.0501
23	E.o	80	35	1	5.21	50	26	50	n	40	15	0	0	r	16	0	r	0	p	2	0.0001
23	E.o	80	36	1	2.45	310	20	47	n	41	13	0	0	r	17	0	r	0	r	7	0.0001
23	E.o	80	37	1	2.48	290	14	46	n	42	15	0	0	p	18	0	r	0	r	7	0.0001
24	E.o	68	38	1	1.78	140	23	48	n	43	19	1	0.0526	r	19	0	r	1	r	4	0.0527
25	E.o	69	39		2.34	320	24	57	n	44	28	5	0.179	r	20	0	r	5	r	8	0.179
25	E.o	69	39	2	2.34	320	21	56	n	45	18	5	0.278	r	21	0	r	5	r	8	0.278
25	E.o	69	40	1	2.08	350	19	41	n	46	21	5	0.238	r	22	0	r	5	r	8	0.238
25	E.o	69	41	1	1.98	0	26	52	n	47	28	3	0.107	r	23	0	r	3	r	1	0.107
25	E.o	69	42	1	2.64	5	22	43	n	48	27	8	0.296	r	1	1	r	8	r	1	0.296
25	E.o	69	43	1	2.81	15	19	35	n	49	11	2	0.182	r	2	0	r	2	r	1	0.182
26	E.o	22	44		3.51	60	3	37	H	50	12	0	0	r	3	0	r	0	r	2	0.0001
26	E.o	22	44	2	3.51	60	36	72	n	51	13	0	0	r	4	0	r	0	r	2	0.0001
27	E.o	21.5	45	1	3.7	21.5	32	50	n	52	35	3	0.0857	r	5	0	r	3	r	1	0.0858
28	E.o	39	46		2.92	50	21	52	n	53	25	0	0	r	6	0	r	0	r	2	0.0001
28	E.o	39	46	2	2.92	50	23	51	n	54	26	6	0.231	r	7	0	r	6	r	2	0.231
28	E.o	39	47	1	2.46	352	23	52	n	55	17	1	0.0588	r	8	0	r	1	r	8	0.0589
28	E.o	39	48	1	2.46	240	16	39	n	56	26	2	0.0769	r	9	0	r	2	r	6	0.077
29	E.o	14	49	1	0.68	10	22	63	n	57	22	1	0.0455	r	10	0	r	1	r	1	0.0456
29	E.o	14	50	1	1.21	300	13	42	n	58	21	0	0	r	11	0	r	0	r	7	0.0001
29	E.o	14	51	1	1.11	245	24	48	n	59	27	0	0	r	12	0	r	0	r	6	0.0001
29	E.o	14	52	1	1.25	155	28	65	n	60	16	0	0	r	13	0	r	0	r	4	0.0001
30	E.o	15	53	1	1.6	290	28	71	n	61	17	4	0.235	r	14	0	r	0	r	7	0.235
31	E.o	83	54	1	3	300	24	54	n	62	32	2	0.0625	r	15	0	r	1	r	7	0.0626
31	E.o	83	55	1	2.71	270	5	31	H	63	16	0	0	r	16	0	r	2	r	6	0.0001
32	E.o	44	56	1	1.9	10	9	30	n						17	0	r	0	r	1
32	E.o	44	57	1	1.79	10	37	77	n						18	0	r			1
32	E.o	44	58	1	1.52	5	24	60	n						19	0	r			1
32	E.o	44	59		0.95	310	18	59	n						20	0	r			7
32	E.o	44	59	2	0.95	310	27	61	n						21	0	r			7
32	E.o	44	60	1	1	310	29	71	n						22	0	r			7
33	E.del	57	61	1	3.14	290	24	55	n						23	0	r			7
34	E.o	79	62	1	3.67	190	24	39	n						24	0	r			5
35	E.o	10	63	1	3.72	30	29	62	n						1	1	r			1
35	E.o	10	64	1	4.88	125	16	48	n						2	0	r			3
36	E.o	79	65	1	2.8	295	24	52	n						3	1	r			7
37	E.o	8.5	66	1	0.69	142	18		n						4	1	r			4
37	E.o	8.5	67	1	0.44	132	5		n						5	1	r			3
38	E.o	84	68	1	1.31	140	20	62	n						6	0	r			4
38	E.o	84	69	2	1.31	140	12	30	n						7	1	r			4
39	E.o	41	70	1	1.86	240	19	43	n						8	0	r			6
41	E.o	3.5	71	1	1.36	120	25	55	n						9	0	r			3
40	E.o	13	72	1	1.2	240			n						10	0	r			6
40	E.o	13	72	2	1.2	240			n						11	0	r			6
40	E.o	13	72	3	1.2	240			n						12	0	r			6
42	E.del	7.5	73	1	1.25	120	32	80	n						13	0	r			3
42	E.del	7.5	73	2	1.25	120	21	57	n						14	0	r			3
42	E.del	7.5	73	3	1.25	120	26	56	n						15	0	r			3
42	E.del	7.5	73	4	1.25	120	29	64	n						16	0	r			3
42	E.del	7.5	73	5	1.25	120	22	62	n						17	0	r			3
42	E.del	7.5	73	6	1.25	120	14	44	n						18	0	r			3
42	E.del	7.5	74	1	1.53	235	22	53	n						19	0	r			6
42	E.del	7.5	75	1	1.66	240	21	50	n						20	0	r			6
42	E.del	7.5	76	1	1.61	245	22	42	n						25	0	r			6
42	E.del	7.5	76	2	1.61	245	21	52	n						1	0	r			6
42	E.del	7.5	76	3	1.61	245	8	41	n						2	0	r			6
42	E.del	7.5	77	1	1.3	210	11	33	n						3	0	r			5
42	E.del	7.5	77	2	1.3	210	17	46	n						4	0	r			5
42	E.del	7.5	77	3	1.3	210	24	68	n						5	0	r			5
42	E.del	7.5	78	1	1.64	210	14	48	n						6	0	r			5
42	E.del	7.5	78	2	1.64	210	23	61	n						7	0	r			5
42	E.del	7.5	78	3	1.64	210	23	50	n						8	0	r			5
42	E.del	7.5	79	1	1.72	210	17	47	n						9	0	r			5
42	E.del	7.5	79	2	1.72	210	10	39	n						10	0	r			5
42	E.del	7.5	80	1	1.78	180	33	77	n						11	0	r			4
42	E.del	7.5	81	1	2.19	180	14	40	n						12	0	r			4
42	E.del	7.5	82	1	2.32	180	12	35	n						13	0	r			4
42	E.del	7.5	82	2	2.32	180	25	38	n						1	0	p			4
42	E.del	7.5	83	1	2.42	180	28	71	n						2	0	p			4
42	E.del	7.5	83	2	2.42	180	27	66	n						3	0	p			4
42	E.del	7.5	84	1	2.55	190	23	47	n						4	0	p			5
42	E.del	7.5	85	1	2.61	174	12	29	n						5	0	p			4
42	E.del	7.5	86	1	2.87	174	17	62	n						6	0	p			4
42	E.del	7.5	87	1	2.63	170	18	51	n						7	0	p			4
42	E.del	7.5	88	1	2.39	170	23	45	n						8	0	p			4
42	E.del	7.5	89	1	1.54	158	22	51	n						9	0	p			4
42	E.del	7.5	90	1	2.14	152	25	58	n						10	0	p			4
42	E.del	7.5	91	1	1.95	150	9	37	n						11	0	p			4
42	E.del	7.5	92	1	1.43	136	18	53	n						12	0	p			4
42	E.del	7.5	92	2	1.43	136			H						13	1	p			4
42	E.del	7.5	92	3	1.43	136			H						14	0	p			4
42	E.del	7.5	92	4	1.43	136			H						15	0	p			4
42	E.del	7.5	93	1	3.12	145	25	61	n						16	0	p			4
42	E.del	7.5	93	2	3.12	145	12	52	n						17	1	p			4
43	E.del	7.5	94	1	2.47	228	13	17	n						18	0	p			6
43	E.del	7.5	94	2	2.47	228			H						19	0	p			6
43	E.del	7.5	94	3	2.47	228			H						20	0	p			6
43	E.del	7.5	95	1	2.76	228			H						21	0	p			6
43	E.del	7.5	96	1	3.72	216	27	71	n						22	0	p			5
43	E.del	7.5	96	2	3.72	216			H						23	0	p			5
44	E.o	64	97	1	3.48	340	11	30	n						24	0	p			8
44	E.o	64	98	1	2.49	350	17	46	n						25	0	p			8
44	E.o	64	98	2	2.49	350			H						1	0	p			8
45	E.o	20.5	99	1	1.36	280	32	78	n						2	0	p			7
45	E.o	20.5	100	1	1.12	250	15	36	n						3	0	p			6
45	E.o	20.5	100	2	1.12	250	25	60	n						4	0	p			6
45	E.o	20.5	100	3	1.12	250	27	61	n						5	0	p			6
45	E.o	20.5	100	4	1.12	250	23	60	n						6	0	p			6
45	E.o	20.5	101	1	1.14	70	29	56	n						7	0	p			2
46	E.o	19.5	102	1	4.18	185	24	52	n						8	0	p			5
46	E.o	19.5	102	2	4.18	185			H						9	0	p			5
46	E.o	19.5	103	1	3.33	180	43	72	n						10	0	p			4
46	E.o	19.5	104	1	3.23	180	27	44	n						11	0	p			4
46	E.o	19.5	105	1	2.62	178	33	60	n						12	0	p			4
46	E.o	19.5	106	1	3.06	174	27	56	n						13	0	p			4
46	E.o	19.5	107	1	3.3	167	25	64	n						14	0	p			4
46	E.o	19.5	108	1	3.34	164	16	40	n						15	0	p			4
46	E.o	19.5	109	1	3.22	160	29	68	n						16	0	p			4
46	E.o	19.5	109	2	3.22	160			H						17	0	p			4
46	E.o	19.5	110	1	3.53	160	17	38	n						18	0	p			4
46	E.o	19.5	110	2	3.53	160	31	61	n						19	0	p			4
46	E.o	19.5	111	1	3.48	158	12	37	n						20	0	p			4
46	E.o	19.5	111	2	3.48	158	7	26	n						1	0	r			4
46	E.o	19.5	112	1	1.24	160	17	48	n						2	0	r			4
46	E.o	19.5	112	2	1.24	160	35	78	n						3	0	r			4
46	E.o	19.5	113	1	1	140	19	46	n						4	0	r			4
46	E.o	19.5	114	1	0.96	108	32	63	n						5	0	r			3
46	E.o	19.5	115	1	1.83	107	18	41	n						6	0	r			3
46	E.o	19.5	115	2	1.83	107	22	51	n						7	0	r			3
46	E.o	19.5	116	1	1.18	104	12	40	n						8	0	r			3
46	E.o	19.5	117	1	0.66	330	10	19	n						9	0	r			8
46	E.o	19.5	117	2	0.66	330	15	31	n						10	0	r			8
46	E.o	19.5	117	3	0.66	330	16	36	n						11	0	r			8
46	E.o	19.5	117	4	0.66	330			H						12	0	r			8
47	E.o	62	118	1	3.91	5	21	51	n						13	0	r			1
47	E.o	62	119	1	3.85	8	14	45	n						14	0	r			1
47	E.o	62	120	2	3.85	8	16	44	n						15	0	r			1
47	E.o	62	120	3	3.85	8	12	28	n						16	0	r			1
47	E.o	62	120	1	4.17	20	34	77	n						17	0	r			1
47	E.o	62	121	1	3.2	350	14	34	n						18	0	r			8
47	E.o	62	122	1	3.35	0	17	40	n						19	0	r			1
47	E.o	62	123	1	3.1	324	28	65	n						20	0	r			8
47	E.o	62	124	1	3.08	324	20	32	n						21	0	r			8
47	E.o	62	125	1	3.4	324	23	59	n						22	0	r			8
47	E.o	62	125	2	3.4	324	13	48	n						23	0	r			8
47	E.o	62	125	3	3.4	324	16	46	n						24	0	r			8
47	E.o	62	126	1	3	332	27	33	n						25	0	r			8
47	E.o	62	127	1	1.9	305	11	33	n						26	0	r			7
47	E.o	62	128	1	1.65	290	15	37	n						27	0	r			7
47	E.o	62	129	1	1.88	290	28	67	n						1	0	r			7
47	E.o	62	130	1	2.45	284	1	7	n						2	0	r			7
47	E.o	62	131	1	2.46	290	11	34	n						3	0	r			7
47	E.o	62	132	1	3.53	284	6	35	n						4	0	r			7
47	E.o	62	132	2	3.53	284	14	42	n						5	0	r			7
47	E.o	62	132	3	3.53	284	28	66	n						6	0	r			7
47	E.o	62	132	4	3.53	284	26	63	n						7	0	r			7
47	E.o	62	133	1	3.53	284	30	62	n						8	0	r			7
47	E.o	62	134	1	1.11	285	18	52	n						9	0	r			7
47	E.o	62	135	1	1.57	250	26	68	n						10	0	r			6
47	E.o	62	136	1	1.55	220	33	71	n						11	0	r			5
47	E.o	62	137	1	2.62	220	20	50	n						12	1	r			5
47	E.o	62	137	2	2.62	220	20	57	n						13	0	r			5
47	E.o	62	137	3	2.62	220	23	58	n						14	0	r			5
47	E.o	62	137	4	2.62	220	6	21	n						15	0	r			5
47	E.o	62	137	5	2.62	220	30	65	n						16	0	r			5
47	E.o	62	138	1	2.4	170	20	53	n						17	0	r			4
47	E.o	62	139	1	2.65	166	21	50	n						18	0	r			4
47	E.o	62	140	1	1.75	146	19	50	n						19	0	r			4
47	E.o	62	141	1	3	143	19	47	n						20	0	r			4
47	E.o	62	142	1	3.4	143	31	70	n						21	0	r			4
															22	0	r
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															25	0	r
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library(betareg) # El paquete para hacer regresión beta

---

Regresión beta

from this webpage: https://binalongbungalows.wordpress.com/tasmanian-orchids/dipodium-roseum-rosy-hyacinth-orchid-0615-web/

Los datos provienen de una especie de orquidea de Autralia, Dipodium roseum, recolectado por RLT en 2004-2005. Vamos a evaluar la relación entre el número de flores y la proporción de frutos por planta. El primer paso es asegarar que no haya valores de 0 y 1. En este caso no hay ni una planta que tiene 100% de frutos, pero si hay individuos que tienen cero frutos.

• RECUERDA x >0 y <1. NO se acepta 0 o 1. Entonces a los valores de 0 se le puede añadir un valor mínimo como 0.001 y a los 1 restar 0.001. En realidad esta modificación no impacta la interpretación de los resultados.

• se remueva también del archivo los NA.

• Nota que el modelo se construye como un modelo lineal betareg(y~x, data =na.omit(df)). Las variables del archivo son PropFR, el proporción de frutos (número de frutos/números de flores) por cada individuo y el número de flores, Number_of_Flowers.

head(dipodium)

Tree Number	Tree species	DBH	Plant number	Ramet number	Distance	Orientation	Number_of_Flowers	Height_Inflo	Herbivory	RowPosition_NF	Number_Flowers_position	Number_of_fruits	Perc_FR_set	pardalinum_or_roseum	Fruit_position_effect	Frutos_si_o_no	P_or_R_Infl_Lenght	Num of fruits	Species_Name	Cardinal orientation	PropFR
1	E.o	75	1	1	2.47	40	11	35	n	1	24	0	0	r	1	0	r	0	r	1	0.0001
1	E.o	76	2	1	1.97	50	19	47	n	2	23	0	0	r	2	0	r	0	r	2	0.0001
2	E.o	76	3	1	1.95	350	18	63	n	3	25	1	0.04	r	3	0	r	1	r	8	0.0401
3	E.o	58	4	1	3.24	210	24	47	n	4	20	5	0.25	r	4	0	r	5	r	5	0.25
4	E.o		5	1	0.85	80	25	61	n	5	13	0	0	r	5	0	r	0	r	2	0.0001
5	E.o	59	6	1	2.62	160	17	35	n	6	25	2	0.08	p	6	0	r	2	p	4	0.0801

library(tidyverse)
dipodium$PropFR=dipodium$Perc_FR_set+0.0001 # solucionar para remover los cero
#dipodium$PropFR
dipodium2=dipodium %>% 
  select(PropFR, Number_of_Flowers,Height_Inflo, Distance) %>% 
  filter(complete.cases(PropFR, Number_of_Flowers,Height_Inflo, Distance))
#dipodium2
write.csv(x=dipodium2, file="dipodium2.csv")


library(readr)
dipodium2 <- read_csv("Data/dipodium2.csv")

## Warning: Missing column names filled in: 'X1' [1]

## 
## ── Column specification ────────────────────────────────────────────────────────
## cols(
##   X1 = col_double(),
##   PropFR = col_double(),
##   Number_of_Flowers = col_double(),
##   Height_Inflo = col_double(),
##   Distance = col_double()
## )

modelpropFr=betareg(PropFR~Number_of_Flowers+Height_Inflo+Distance, data =na.omit(dipodium2))
summary(modelpropFr)

## 
## Call:
## betareg(formula = PropFR ~ Number_of_Flowers + Height_Inflo + Distance, 
##     data = na.omit(dipodium2))
## 
## Standardized weighted residuals 2:
##     Min      1Q  Median      3Q     Max 
## -3.8613 -0.4046  0.2672  0.8535  1.2798 
## 
## Coefficients (mean model with logit link):
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept)       -3.796016   0.727139  -5.220 1.78e-07 ***
## Number_of_Flowers  0.076200   0.028247   2.698  0.00698 ** 
## Height_Inflo       0.006054   0.017847   0.339  0.73444    
## Distance          -0.111010   0.093825  -1.183  0.23674    
## 
## Phi coefficients (precision model with identity link):
##       Estimate Std. Error z value Pr(>|z|)    
## (phi)   4.8382     0.9982   4.847 1.25e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Type of estimator: ML (maximum likelihood)
## Log-likelihood: 113.9 on 5 Df
## Pseudo R-squared: 0.2757
## Number of iterations: 19 (BFGS) + 2 (Fisher scoring)

Visualizar un grafico de regresión beta

dipodiumbeta=dipodium2[,c("Number_of_Flowers","PropFR")] # crear un df con solamente las columnas de interes 

 dp2=dipodiumbeta[complete.cases(dipodiumbeta),] # remover los "NA" 
 
modelpropFr=betareg(PropFR~Number_of_Flowers, data=dp2) # El modelo con solamente la explicativa
summary(modelpropFr)

## 
## Call:
## betareg(formula = PropFR ~ Number_of_Flowers, data = dp2)
## 
## Standardized weighted residuals 2:
##     Min      1Q  Median      3Q     Max 
## -3.3221 -0.3181  0.2414  0.8225  1.2346 
## 
## Coefficients (mean model with logit link):
##                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept)       -3.88360    0.44251  -8.776  < 2e-16 ***
## Number_of_Flowers  0.08259    0.01803   4.581 4.62e-06 ***
## 
## Phi coefficients (precision model with identity link):
##       Estimate Std. Error z value Pr(>|z|)    
## (phi)   4.6947     0.9699    4.84  1.3e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Type of estimator: ML (maximum likelihood)
## Log-likelihood: 112.9 on 3 Df
## Pseudo R-squared: 0.2538
## Number of iterations: 18 (BFGS) + 1 (Fisher scoring)

 #head(dp2)
#dp2$PropFR
predict(modelpropFr, type = "response") # calcular los valores estimados (predichos)

##          1          2          3          4          5          6          7 
## 0.02568523 0.02783519 0.03015954 0.04856508 0.05679268 0.05679268 0.05679268 
##          8          9         10         11         12         13         14 
## 0.06138242 0.06138242 0.06138242 0.06138242 0.06138242 0.06138242 0.06631700 
##         15         16         17         18         19         20         21 
## 0.06631700 0.07161801 0.07161801 0.07161801 0.07161801 0.07730766 0.07730766 
##         22         23         24         25         26         27         28 
## 0.07730766 0.08340872 0.08340872 0.08994433 0.08994433 0.08994433 0.08994433 
##         29         30         31         32         33         34         35 
## 0.09693789 0.10441284 0.10441284 0.10441284 0.10441284 0.10441284 0.11239245 
##         36         37         38         39         40         41         42 
## 0.11239245 0.12089957 0.12089957 0.12089957 0.12089957 0.12089957 0.12089957 
##         43         44         45         46         47         48         49 
## 0.12995632 0.12995632 0.12995632 0.12995632 0.12995632 0.13958381 0.14980172 
##         50         51         52         53         54         55         56 
## 0.14980172 0.14980172 0.17207828 0.17207828 0.17207828 0.17207828 0.19690033 
##         57         58         59         60         61         62 
## 0.19690033 0.22433274 0.22433274 0.23903102 0.27035714 0.28695536

dp2$response=predict(modelpropFr, type = "response")
#dp2$link=predict(modelpropFr, type = "link")
dp2$precision=predict(modelpropFr, type = "precision")
dp2$variance=predict(modelpropFr, type = "variance")
dp2$quantile_.01=predict(modelpropFr, type = "quantile", at = c(0.01))
dp2$quantile_.05=predict(modelpropFr, type = "quantile", at = c(0.05))
dp2$quantile_.10=predict(modelpropFr, type = "quantile", at = c(0.10))
dp2$quantile_.15=predict(modelpropFr, type = "quantile", at = c(0.15))
dp2$quantile_.20=predict(modelpropFr, type = "quantile", at = c(0.20))
dp2$quantile_.25=predict(modelpropFr, type = "quantile", at = c(0.25))
dp2$quantile_.30=predict(modelpropFr, type = "quantile", at = c(0.30))
dp2$quantile_.35=predict(modelpropFr, type = "quantile", at = c(0.35))
dp2$quantile_.40=predict(modelpropFr, type = "quantile", at = c(0.40))
dp2$quantile_.45=predict(modelpropFr, type = "quantile", at = c(0.45))
dp2$quantile_.50=predict(modelpropFr, type = "quantile", at = c(0.50))
dp2$quantile_.55=predict(modelpropFr, type = "quantile", at = c(0.55))
dp2$quantile_.60=predict(modelpropFr, type = "quantile", at = c(0.60))
dp2$quantile_.65=predict(modelpropFr, type = "quantile", at = c(0.65))
dp2$quantile_.70=predict(modelpropFr, type = "quantile", at = c(0.70))
dp2$quantile_.75=predict(modelpropFr, type = "quantile", at = c(0.75))
dp2$quantile_.80=predict(modelpropFr, type = "quantile", at = c(0.80))
dp2$quantile_.85=predict(modelpropFr, type = "quantile", at = c(0.85))
dp2$quantile_.90=predict(modelpropFr, type = "quantile", at = c(0.90))
dp2$quantile_.95=predict(modelpropFr, type = "quantile", at = c(0.95))
dp2$quantile_.99=predict(modelpropFr, type = "quantile", at = c(0.99))
dp2

Number_of_Flowers	PropFR	response	precision	variance	quantile_.01	quantile_.05	quantile_.10	quantile_.15	quantile_.20	quantile_.25	quantile_.30	quantile_.35	quantile_.40	quantile_.45	quantile_.50	quantile_.55	quantile_.60	quantile_.65	quantile_.70	quantile_.75	quantile_.80	quantile_.85	quantile_.90	quantile_.95	quantile_.99
3	0.0001	0.0257	4.69	0.00439	3.86e-18	2.42e-12	7.58e-10	2.19e-08	2.38e-07	1.51e-06	6.86e-06	2.46e-05	7.46e-05	0.000198	0.000475	0.00105	0.00217	0.00424	0.00792	0.0143	0.0253	0.0444	0.0792	0.153	0.342
4	0.0001	0.0278	4.69	0.00475	7.44e-17	1.66e-11	3.34e-09	7.44e-08	6.72e-07	3.71e-06	1.5e-05	4.87e-05	0.000135	0.000333	0.000748	0.00155	0.00304	0.00565	0.0101	0.0175	0.0299	0.0506	0.0872	0.163	0.353
5	0.0001	0.0302	4.69	0.00514	1.14e-15	9.81e-11	1.31e-08	2.3e-07	1.75e-06	8.48e-06	3.07e-05	9.13e-05	0.000235	0.000539	0.00114	0.00224	0.00416	0.0074	0.0127	0.0212	0.0349	0.0572	0.0957	0.173	0.364
11	0.0001	0.0486	4.69	0.00811	2.75e-10	3.2e-07	6.69e-06	3.96e-05	0.00014	0.000372	0.000829	0.00163	0.00295	0.00497	0.00795	0.0122	0.0182	0.0265	0.0378	0.0534	0.0751	0.106	0.155	0.242	0.434
13	0.0358	0.0568	4.69	0.00941	5.29e-09	2.21e-06	2.98e-05	0.000136	0.000401	0.000928	0.00184	0.0033	0.00547	0.00859	0.0129	0.0187	0.0265	0.0368	0.0503	0.0683	0.0926	0.127	0.177	0.267	0.458
13	0.0939	0.0568	4.69	0.00941	5.29e-09	2.21e-06	2.98e-05	0.000136	0.000401	0.000928	0.00184	0.0033	0.00547	0.00859	0.0129	0.0187	0.0265	0.0368	0.0503	0.0683	0.0926	0.127	0.177	0.267	0.458
13	0.0001	0.0568	4.69	0.00941	5.29e-09	2.21e-06	2.98e-05	0.000136	0.000401	0.000928	0.00184	0.0033	0.00547	0.00859	0.0129	0.0187	0.0265	0.0368	0.0503	0.0683	0.0926	0.127	0.177	0.267	0.458
14	0.0001	0.0614	4.69	0.0101	1.96e-08	5.21e-06	5.77e-05	0.000236	0.000641	0.00139	0.00263	0.00451	0.00723	0.011	0.016	0.0227	0.0314	0.0427	0.0574	0.0765	0.102	0.137	0.189	0.28	0.47
14	0.364	0.0614	4.69	0.0101	1.96e-08	5.21e-06	5.77e-05	0.000236	0.000641	0.00139	0.00263	0.00451	0.00723	0.011	0.016	0.0227	0.0314	0.0427	0.0574	0.0765	0.102	0.137	0.189	0.28	0.47
14	0.105	0.0614	4.69	0.0101	1.96e-08	5.21e-06	5.77e-05	0.000236	0.000641	0.00139	0.00263	0.00451	0.00723	0.011	0.016	0.0227	0.0314	0.0427	0.0574	0.0765	0.102	0.137	0.189	0.28	0.47
14	0.131	0.0614	4.69	0.0101	1.96e-08	5.21e-06	5.77e-05	0.000236	0.000641	0.00139	0.00263	0.00451	0.00723	0.011	0.016	0.0227	0.0314	0.0427	0.0574	0.0765	0.102	0.137	0.189	0.28	0.47
14	0.231	0.0614	4.69	0.0101	1.96e-08	5.21e-06	5.77e-05	0.000236	0.000641	0.00139	0.00263	0.00451	0.00723	0.011	0.016	0.0227	0.0314	0.0427	0.0574	0.0765	0.102	0.137	0.189	0.28	0.47
14	0.0001	0.0614	4.69	0.0101	1.96e-08	5.21e-06	5.77e-05	0.000236	0.000641	0.00139	0.00263	0.00451	0.00723	0.011	0.016	0.0227	0.0314	0.0427	0.0574	0.0765	0.102	0.137	0.189	0.28	0.47
15	0.0001	0.0663	4.69	0.0109	6.54e-08	1.15e-05	0.000107	0.000392	0.000989	0.00203	0.00366	0.00605	0.00937	0.0138	0.0197	0.0273	0.037	0.0493	0.0651	0.0854	0.112	0.149	0.202	0.293	0.483
15	0.179	0.0663	4.69	0.0109	6.54e-08	1.15e-05	0.000107	0.000392	0.000989	0.00203	0.00366	0.00605	0.00937	0.0138	0.0197	0.0273	0.037	0.0493	0.0651	0.0854	0.112	0.149	0.202	0.293	0.483
16	0.0371	0.0716	4.69	0.0117	1.99e-07	2.39e-05	0.000188	0.000627	0.00148	0.00288	0.00499	0.00794	0.0119	0.0172	0.0239	0.0324	0.0431	0.0565	0.0733	0.0948	0.123	0.16	0.215	0.307	0.496
16	0.0001	0.0716	4.69	0.0117	1.99e-07	2.39e-05	0.000188	0.000627	0.00148	0.00288	0.00499	0.00794	0.0119	0.0172	0.0239	0.0324	0.0431	0.0565	0.0733	0.0948	0.123	0.16	0.215	0.307	0.496
16	0.125	0.0716	4.69	0.0117	1.99e-07	2.39e-05	0.000188	0.000627	0.00148	0.00288	0.00499	0.00794	0.0119	0.0172	0.0239	0.0324	0.0431	0.0565	0.0733	0.0948	0.123	0.16	0.215	0.307	0.496
16	0.077	0.0716	4.69	0.0117	1.99e-07	2.39e-05	0.000188	0.000627	0.00148	0.00288	0.00499	0.00794	0.0119	0.0172	0.0239	0.0324	0.0431	0.0565	0.0733	0.0948	0.123	0.16	0.215	0.307	0.496
17	0.0801	0.0773	4.69	0.0125	5.56e-07	4.69e-05	0.000317	0.00097	0.00215	0.00399	0.00664	0.0102	0.015	0.021	0.0286	0.0381	0.0498	0.0642	0.0822	0.105	0.134	0.172	0.228	0.321	0.509
17	0.333	0.0773	4.69	0.0125	5.56e-07	4.69e-05	0.000317	0.00097	0.00215	0.00399	0.00664	0.0102	0.015	0.021	0.0286	0.0381	0.0498	0.0642	0.0822	0.105	0.134	0.172	0.228	0.321	0.509
17	0.0001	0.0773	4.69	0.0125	5.56e-07	4.69e-05	0.000317	0.00097	0.00215	0.00399	0.00664	0.0102	0.015	0.021	0.0286	0.0381	0.0498	0.0642	0.0822	0.105	0.134	0.172	0.228	0.321	0.509
18	0.0401	0.0834	4.69	0.0134	1.44e-06	8.76e-05	0.000515	0.00145	0.00304	0.00541	0.00868	0.013	0.0185	0.0254	0.034	0.0444	0.0571	0.0726	0.0916	0.115	0.145	0.185	0.242	0.335	0.522
18	0.0001	0.0834	4.69	0.0134	1.44e-06	8.76e-05	0.000515	0.00145	0.00304	0.00541	0.00868	0.013	0.0185	0.0254	0.034	0.0444	0.0571	0.0726	0.0916	0.115	0.145	0.185	0.242	0.335	0.522
19	0.0001	0.0899	4.69	0.0144	3.45e-06	0.000156	0.000808	0.00212	0.0042	0.00718	0.0112	0.0163	0.0226	0.0305	0.0399	0.0514	0.0651	0.0816	0.102	0.126	0.158	0.198	0.256	0.35	0.535
19	0.0001	0.0899	4.69	0.0144	3.45e-06	0.000156	0.000808	0.00212	0.0042	0.00718	0.0112	0.0163	0.0226	0.0305	0.0399	0.0514	0.0651	0.0816	0.102	0.126	0.158	0.198	0.256	0.35	0.535
19	0.238	0.0899	4.69	0.0144	3.45e-06	0.000156	0.000808	0.00212	0.0042	0.00718	0.0112	0.0163	0.0226	0.0305	0.0399	0.0514	0.0651	0.0816	0.102	0.126	0.158	0.198	0.256	0.35	0.535
19	0.182	0.0899	4.69	0.0144	3.45e-06	0.000156	0.000808	0.00212	0.0042	0.00718	0.0112	0.0163	0.0226	0.0305	0.0399	0.0514	0.0651	0.0816	0.102	0.126	0.158	0.198	0.256	0.35	0.535
20	0.0001	0.0969	4.69	0.0154	7.76e-06	0.000267	0.00123	0.003	0.00568	0.00935	0.0141	0.0201	0.0273	0.0361	0.0465	0.059	0.0737	0.0913	0.112	0.138	0.17	0.212	0.27	0.365	0.549
21	0.179	0.104	4.69	0.0164	1.64e-05	0.000438	0.00181	0.00415	0.00752	0.012	0.0176	0.0244	0.0326	0.0424	0.0538	0.0673	0.0831	0.102	0.124	0.151	0.184	0.226	0.285	0.38	0.563
21	0.154	0.104	4.69	0.0164	1.64e-05	0.000438	0.00181	0.00415	0.00752	0.012	0.0176	0.0244	0.0326	0.0424	0.0538	0.0673	0.0831	0.102	0.124	0.151	0.184	0.226	0.285	0.38	0.563
21	0.273	0.104	4.69	0.0164	1.64e-05	0.000438	0.00181	0.00415	0.00752	0.012	0.0176	0.0244	0.0326	0.0424	0.0538	0.0673	0.0831	0.102	0.124	0.151	0.184	0.226	0.285	0.38	0.563
21	0.278	0.104	4.69	0.0164	1.64e-05	0.000438	0.00181	0.00415	0.00752	0.012	0.0176	0.0244	0.0326	0.0424	0.0538	0.0673	0.0831	0.102	0.124	0.151	0.184	0.226	0.285	0.38	0.563
21	0.0001	0.104	4.69	0.0164	1.64e-05	0.000438	0.00181	0.00415	0.00752	0.012	0.0176	0.0244	0.0326	0.0424	0.0538	0.0673	0.0831	0.102	0.124	0.151	0.184	0.226	0.285	0.38	0.563
22	0.296	0.112	4.69	0.0175	3.28e-05	0.000694	0.00259	0.00562	0.00978	0.0151	0.0216	0.0294	0.0386	0.0494	0.0618	0.0763	0.0931	0.113	0.136	0.164	0.198	0.241	0.301	0.396	0.577
22	0.0456	0.112	4.69	0.0175	3.28e-05	0.000694	0.00259	0.00562	0.00978	0.0151	0.0216	0.0294	0.0386	0.0494	0.0618	0.0763	0.0931	0.113	0.136	0.164	0.198	0.241	0.301	0.396	0.577
23	0.333	0.121	4.69	0.0187	6.23e-05	0.00106	0.00362	0.00746	0.0125	0.0188	0.0263	0.0351	0.0453	0.057	0.0705	0.086	0.104	0.124	0.149	0.177	0.212	0.256	0.317	0.412	0.591
23	0.26	0.121	4.69	0.0187	6.23e-05	0.00106	0.00362	0.00746	0.0125	0.0188	0.0263	0.0351	0.0453	0.057	0.0705	0.086	0.104	0.124	0.149	0.177	0.212	0.256	0.317	0.412	0.591
23	0.105	0.121	4.69	0.0187	6.23e-05	0.00106	0.00362	0.00746	0.0125	0.0188	0.0263	0.0351	0.0453	0.057	0.0705	0.086	0.104	0.124	0.149	0.177	0.212	0.256	0.317	0.412	0.591
23	0.0527	0.121	4.69	0.0187	6.23e-05	0.00106	0.00362	0.00746	0.0125	0.0188	0.0263	0.0351	0.0453	0.057	0.0705	0.086	0.104	0.124	0.149	0.177	0.212	0.256	0.317	0.412	0.591
23	0.231	0.121	4.69	0.0187	6.23e-05	0.00106	0.00362	0.00746	0.0125	0.0188	0.0263	0.0351	0.0453	0.057	0.0705	0.086	0.104	0.124	0.149	0.177	0.212	0.256	0.317	0.412	0.591
23	0.0589	0.121	4.69	0.0187	6.23e-05	0.00106	0.00362	0.00746	0.0125	0.0188	0.0263	0.0351	0.0453	0.057	0.0705	0.086	0.104	0.124	0.149	0.177	0.212	0.256	0.317	0.412	0.591
24	0.25	0.13	4.69	0.0199	0.000113	0.00158	0.00496	0.00972	0.0158	0.023	0.0316	0.0414	0.0527	0.0655	0.08	0.0964	0.115	0.137	0.162	0.191	0.227	0.272	0.333	0.428	0.605
24	0.0456	0.13	4.69	0.0199	0.000113	0.00158	0.00496	0.00972	0.0158	0.023	0.0316	0.0414	0.0527	0.0655	0.08	0.0964	0.115	0.137	0.162	0.191	0.227	0.272	0.333	0.428	0.605
24	0.179	0.13	4.69	0.0199	0.000113	0.00158	0.00496	0.00972	0.0158	0.023	0.0316	0.0414	0.0527	0.0655	0.08	0.0964	0.115	0.137	0.162	0.191	0.227	0.272	0.333	0.428	0.605
24	0.0001	0.13	4.69	0.0199	0.000113	0.00158	0.00496	0.00972	0.0158	0.023	0.0316	0.0414	0.0527	0.0655	0.08	0.0964	0.115	0.137	0.162	0.191	0.227	0.272	0.333	0.428	0.605
24	0.0626	0.13	4.69	0.0199	0.000113	0.00158	0.00496	0.00972	0.0158	0.023	0.0316	0.0414	0.0527	0.0655	0.08	0.0964	0.115	0.137	0.162	0.191	0.227	0.272	0.333	0.428	0.605
25	0.25	0.14	4.69	0.0211	0.000195	0.00229	0.00664	0.0125	0.0196	0.0279	0.0376	0.0485	0.0608	0.0746	0.0902	0.108	0.127	0.15	0.176	0.206	0.243	0.289	0.35	0.445	0.62
26	0.0501	0.15	4.69	0.0224	0.000325	0.00322	0.00872	0.0157	0.024	0.0335	0.0443	0.0563	0.0697	0.0846	0.101	0.12	0.14	0.164	0.191	0.222	0.259	0.306	0.367	0.462	0.634
26	0.31	0.15	4.69	0.0224	0.000325	0.00322	0.00872	0.0157	0.024	0.0335	0.0443	0.0563	0.0697	0.0846	0.101	0.12	0.14	0.164	0.191	0.222	0.259	0.306	0.367	0.462	0.634
26	0.107	0.15	4.69	0.0224	0.000325	0.00322	0.00872	0.0157	0.024	0.0335	0.0443	0.0563	0.0697	0.0846	0.101	0.12	0.14	0.164	0.191	0.222	0.259	0.306	0.367	0.462	0.634
28	0.0691	0.172	4.69	0.025	0.00081	0.00599	0.0143	0.024	0.0349	0.0469	0.06	0.0743	0.0899	0.107	0.125	0.146	0.168	0.194	0.222	0.255	0.294	0.341	0.403	0.497	0.664
28	0.22	0.172	4.69	0.025	0.00081	0.00599	0.0143	0.024	0.0349	0.0469	0.06	0.0743	0.0899	0.107	0.125	0.146	0.168	0.194	0.222	0.255	0.294	0.341	0.403	0.497	0.664
28	0.22	0.172	4.69	0.025	0.00081	0.00599	0.0143	0.024	0.0349	0.0469	0.06	0.0743	0.0899	0.107	0.125	0.146	0.168	0.194	0.222	0.255	0.294	0.341	0.403	0.497	0.664
28	0.235	0.172	4.69	0.025	0.00081	0.00599	0.0143	0.024	0.0349	0.0469	0.06	0.0743	0.0899	0.107	0.125	0.146	0.168	0.194	0.222	0.255	0.294	0.341	0.403	0.497	0.664
30	0.1	0.197	4.69	0.0278	0.00178	0.0103	0.0222	0.035	0.0488	0.0634	0.079	0.0956	0.113	0.132	0.153	0.175	0.2	0.226	0.256	0.29	0.33	0.378	0.441	0.533	0.694
30	0.154	0.197	4.69	0.0278	0.00178	0.0103	0.0222	0.035	0.0488	0.0634	0.079	0.0956	0.113	0.132	0.153	0.175	0.2	0.226	0.256	0.29	0.33	0.378	0.441	0.533	0.694
32	0.111	0.224	4.69	0.0306	0.00353	0.0166	0.0327	0.049	0.0659	0.0833	0.101	0.12	0.14	0.161	0.184	0.208	0.234	0.262	0.293	0.328	0.369	0.418	0.48	0.571	0.725
32	0.0858	0.224	4.69	0.0306	0.00353	0.0166	0.0327	0.049	0.0659	0.0833	0.101	0.12	0.14	0.161	0.184	0.208	0.234	0.262	0.293	0.328	0.369	0.418	0.48	0.571	0.725
33	0.154	0.239	4.69	0.0319	0.00481	0.0206	0.039	0.0573	0.0757	0.0946	0.114	0.134	0.155	0.177	0.2	0.225	0.252	0.281	0.313	0.348	0.389	0.438	0.5	0.589	0.74
35	0.25	0.27	4.69	0.0346	0.0084	0.0306	0.0541	0.0763	0.0981	0.12	0.142	0.164	0.187	0.211	0.236	0.262	0.29	0.32	0.353	0.39	0.431	0.479	0.54	0.628	0.77
36	0.1	0.287	4.69	0.0359	0.0108	0.0366	0.0629	0.0872	0.111	0.134	0.157	0.18	0.204	0.229	0.255	0.282	0.311	0.341	0.374	0.411	0.452	0.501	0.561	0.647	0.785

#modelpropFr$precision

#quantile_many=predict(modelpropFr, type = "quantile", at=c(.99))
#quantile_many

Al construir la figura para la regresión beta, una de las principales ventajas de utilizar este enfoque es que los cuartiles se calcula con una distribución beta. Por lo tanto, el margen de error NO baja de 0 y NO pasa de 1.

Evalua la siguiente figura en cada x hay una distribución beta, donde la linea roja representa ma mediana, las lineas verdes los cuartiles 25 y 75 y las lineas azules los cuartiles 5 y 95. NOTA que la distribución no es simétrica, y cambia a travez de la regresión.

library(ggplot2)
ggplot(dp2, aes(x=Number_of_Flowers, y=PropFR))+
  geom_point(width = 0.05, height = 0.01)+
  geom_line(aes(y=quantile_.05), linetype="twodash", colour="blue")+
  geom_line(aes(y=quantile_.25),linetype=2, colour="green")+
  geom_line(aes(y=quantile_.50), colour="red")+
  geom_line(aes(y=quantile_.75), linetype=2, colour="green")+
  geom_line(aes(y=quantile_.95), linetype="twodash", colour="blue")+
  ylab("Predicción de la proporción de frutos")+
  xlab("Números de Flores")+
  annotate("text", x=25, y=0.50, label="95th quartile", fontface="italic")+
  annotate("text", x=32, y=0.39, label="75th quartile", fontface="italic")+
  annotate("text", x=33, y=0.14, label="25th quartile", fontface="italic")+
  annotate("text", x=33, y=0.27, label="Median", fontface="italic")+
  annotate("text", x=35, y=-0.02, label="5th quartile", fontface="italic")+
theme(axis.title.y = element_text(colour="grey20",size=20,face="bold"),
        axis.text.x = element_text(colour="grey20",size=20,face="bold"),
        axis.text.y = element_text(colour="grey20",size=20,face="bold"), 
        axis.title.x = element_text(colour="grey20",size=20,face="bold"))+
  theme(legend.position="none")+
  rlt_theme

## Warning: Ignoring unknown parameters: width, height

ggsave("Graficos/Beta_number_flowers.png")

## Saving 7 x 5 in image

Aquí es una representación de las distribuciones beta en las x, número de flores. En rojo es para simular la distribución la proporción esperada de frutos en plantas que tienen 15 flores y la linea azul es para simular la distribución esperada de la proporción de frutos en plantas con 30 flores.
***

Evaluando la distribución de beta para valores específicos de x= Proporción de frutos por plantas basado en la cantidad de flores en la planta.

Seleccionar los diferentes valores de x y calcular el promedio y la varianza y convertir estos en \(\alpha\) y \(\beta\). Con estos parámetros se puede construir la densidad de la distribución por cada valor de x.

Se selecciona valores específicos para la visualizar la distribución, las plantas que tienen 25, 30 y 35 flores. Se tiene que reorganizar los datos para calcular el promedio y la varianza.

dpQ=dp2 %>% 
  select(c(1, 6:26))

dpQ2=dpQ%>% 
  filter(Number_of_Flowers== 13) %>% select(c(2:22))%>% t %>% as.data.frame
dpQ2$Quartiles=c(.01, 0.05, .1, .15, .2, .25, .30, .35, .4, .45, .5, .55, .6, .65,  .7,.75, .8, .85, .9, .95, .99 )

mean(dpQ2$V1, na.rm=FALSE)

## [1] 0.06453931

var(dpQ2$V1, na.rm=FALSE)

## [1] 0.01296751

#dpQ2


ggplot(dpQ2, aes(Quartiles, V1))+
 geom_line()

Usando la varianza calculada en el chunk anterior, se puede calcular el \(\alpha\) y el \(\beta\).

estBetaParams <- function(mu, var) {
  alpha <- ((1 - mu) / var - 1 / mu) * mu ^ 2
  beta <- alpha * (1 / mu - 1)
  return(params = list(alpha = alpha, beta = beta))
}
#mean(Smokers$Y2000P)
#var(Smokers$Y2000P)
estBetaParams(0.2757771,0.04226223)

## $alpha
## [1] 1.027498
## 
## $beta
## [1] 2.698331

---

Producción de los gráficos. Se observa que para las plantas que tienen 25 y 30 flores la densidad esta sesgada a la izquierda, en otra palabra la probabilidad de tener pocas frutos domina la distribuciones.

library(gridExtra)
a=ggplot(dipodium2, aes(PropFR))+
stat_function(aes(x = dipodium2$PropFR, y = ..y..), fun = dbeta, colour="red", n = 62,
                      args = list(shape1 =0.5418068, shape2 =3.135593))+
  annotate("text", label="x=25 flores", x=0.1, y=10)+
  ylab("Beta \nDensity")+
  xlab("Probabilidad de tener frutos")

b=ggplot(dipodium2, aes(PropFR))+
stat_function(aes(x = dipodium2$PropFR, y = ..y..), fun = dbeta, colour="blue", n = 62,
                      args = list(shape1 = 0.7549048, shape2 =2.949404))+
  annotate("text", label="x=30 flores", x=0.1, y=5)+
  ylab("Beta \nDensity")+
  xlab("Probabilidad de tener frutos")

c=ggplot(dipodium2, aes(PropFR))+
stat_function(aes(x = dipodium2$PropFR, y = ..y..), fun = dbeta, colour="black", n = 62,
                      args = list(shape1 = 1.027498, shape2 =2.698331))+
  annotate("text", label="x=35 flores", x=0.1, y=2)+
  ylab("Beta \nDensity")+
  xlab("Probabilidad de tener frutos")
tresDensidad=grid.arrange(a,b,c, ncol=1)

tresDensidad

## TableGrob (3 x 1) "arrange": 3 grobs
##   z     cells    name           grob
## 1 1 (1-1,1-1) arrange gtable[layout]
## 2 2 (2-2,1-1) arrange gtable[layout]
## 3 3 (3-3,1-1) arrange gtable[layout]

ggsave("Graficos/tresDensidad.png")

## Saving 7 x 5 in image

“Activities reported in this website was supported by the National Institute of General Medical Sciences of the National Institutes of Health under Award Number R25GM121270. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.”